I've had some success getting a normal aftermarket leather strap to fit my 5S and thought I'd share.
Any normal 20mm wide strap should fit, with the only challenges being the width of the bars and removing the bars from the watch. Each bar has a T6 Torx (not a T5 as I've seen others state elsewhere on the forum - a T5 might grip, but with significant play and the risk of damaging driver and bar end) head at each end. Use a T6 driver at each end to undo and remove the bar (I wouldn't advise using a single T6 driver and trying to grip the bar to prevent it spinning, as you're likely to end up with idiot marks if you use pliers/grips). At 2mm wide the bars can be a challenge to squeeze in. For rubber/silicone straps a dab of washing liquid to lubricate the pin should be enough. For leather straps I pre-stretched the loop in the strap using first a 5/64 ball-end hex key and then a 3/32 ball-end hex key, which seemed less violent than trying to use a drill. The bars then slid in with reasonable pressure.
Will take some photos once my new straps arrive, as I had to cannibalise one from my analogue watch to test. :)